Quantum size effects on the perpendicular upper critical field in ultrathin lead films

We report the thickness-dependent (in terms of atomic layers) oscillation behavior of the perpendicular upper critical field H-c2 perpendicular to in the ultrathin lead films at the reduced temperature (t=T/T-c). Distinct oscillations of the normal-state resistivity as a function of film thickness have also been observed. Compared with the T-c oscillation, the H-c2 perpendicular to shows a considerable large oscillation amplitude and a pi phase shift. The oscillatory mean free path caused by the quantum size effect plays a role in H-c2 perpendicular to oscillation.